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Langmuir 2008, 24, 7912-7922
New Method for Atomistic Modeling of the Microstructure of Activated Carbons Using Hybrid Reverse Monte Carlo Simulation Thanh X. Nguyen,† Nathalie Cohaut,‡ Jun-Seok Bae,† and Suresh K. Bhatia*,† DiVision of Chemical Engineering, The UniVersity of Queensland, St. Lucia, Brisbane QLD 4067, Australia, and Centre de Recherche sur la Matie`re DiVise´e, UMR 6619 1b rue de la Fe´rollerie, 45071 Orle´ans Cedex 2, France ReceiVed January 31, 2008. ReVised Manuscript ReceiVed April 19, 2008 We propose a new hybrid reverse Monte Carlo (HRMC) procedure for atomistic modeling of the microstructure of activated carbons whereby the guessed configuration for the HRMC construction simulation is generated using the characterization results (pore size and pore wall thickness distributions) obtained by the interpretation of argon adsorption at 87 K using our improved version of the slit-pore model, termed the finite wall thickness (FWT) model (Nguyen, T. X.; Bhatia, S. K. Langmuir 2004, 20, 3532). This procedure overcomes limitations arising from the use of shortrange potentials in the conventional HRMC method, which make the latter unsuitable for carbons such as activated carbon fibers that are anisotropic with medium-range ordering induced by their complex pore structure. The newly proposed approach is applied specifically for the atomistic construction of an activated carbon fiber ACF15, provided by Kynol Corporation (Nguyen, T. X.; Bhatia, S. K. Carbon 2005, 43, 775). It is found that the PSD of the ACF15’s constructed microstructure is in good agreement with that determined using argon adsorption at 87 K. Furthermore, we have also found that the use of the Lennard-Jones (LJ) carbon-fluid interaction well depth obtained from scaling the flat graphite surface-fluid interaction well depth taken from Steele (Steele, W. A. Surf. Sci. 1973, 36, 317) provides an excellent prediction of experimental adsorption data including the differential heat of adsorption of simple gases (Ar, N2, CH4, CO2) over a wide range of temperatures and pressures. This finding is in agreement with the enhancement of the LJ carbon-fluid well depth due to the curvature of the carbon surface, found by the use of ab initio calculations (Klauda, J. B.; Jiang, J.; Sandler, S. I. J. Phys. Chem. B 2004, 108, 9842).
1. Introduction Porous carbons have long been used for gas- and liquid-phase adsorptive separations as well as the storage of volatile compounds because of their high surface area and strong adsorption force field. It is well recognized that the microstructure of porous carbons governs adsorption equilibrium and dynamic behavior. Accordingly, the synthesis and manufacture of carbons with the desired adsorptive properties require a reliable characterization of the internal structure of the carbon, which can be used to predict adsorption equilibrium and kinetics from a mature understanding of the behavior of fluids in confined spaces. In general, the microstructure of activated carbons normally indicates that they contain pores formed between curled carbon layers having various degrees of curvature that can even form fullerenelike structures, as have been observed in high-temperature heatedactivated carbons by high-resolution transmission microscopy (HRTEM).5–7 From this observation, the slit-pore model composed of a set of unconnected slitlike pores is widely accepted for the characterization of the microstructure of porous carbons using gas physisorption.1,8,9 Meanwhile, fullerene-like atomistic models are also used to represent the microstructure of hard * To whom correspondence may be addressed. E-mail: s.bhatia@ eng.uq.edu.au. † The University of Queensland. ‡ Centre de Recherche sur la Matie`re Divise´e.
(1) Nguyen, T. X.; Bhatia, S. K. Langmuir 2004, 20, 3532. (2) Nguyen, T. X.; Bhatia, S. K. Carbon 2005, 43, 775. (3) Steele, W. A. Surf. Sci. 1973, 36, 317. (4) Klauda, J. B.; Jiang, J.; Sandler, S. I. J. Phys. Chem. B 2004, 108, 9842. (5) Harris, P. J. F.; Tsang, S. C. Philos. Mag. A 1997, 76, 667. (6) Harris, P. J. F.; Burian, A.; Duber, S. Philos. Mag. Lett. 2000, 80, 381. (7) Harris, P. J. F. Philos. Mag. 2004, 84, 3159. (8) Lastoskie, C. M.; Gubbins, K. E.; Quirke, N. J. Phys. Chem. 1993, 97, 4786. (9) Ravikovitch, P. I.; Vishnyakov, A.; Russo, R.; Neimark, A. V. Langmuir 2000, 16, 2311.
activated carbons prepared by high-temperature treatment of the activated carbons.10,11 Despite such a crude approximation of the slit-pore model to the real porous carbon structure, it has been shown that its recently improved version in the form of our finite wall thickness (FWT) model, whereby pore size and pore wall thickness distributions are simultaneously characterized, provides a correct prediction of the adsorption equilibrium of simple gases over a wide range of temperatures and pressures in several activated carbons, which are free of pore-accessibility problems.12,13 However, the slitpore model in general disregards surface roughness as well as the complexities of pore network accessibility. This leads to the inappropriateness of the model when used for the study of adsorption equilibrium and dynamics in porous carbons whose microstructure has a pore-accessibility problem for some adsorbates14,15 as well as the inability of the model to determine transport diffusivity through nanoporous carbons without a knowledge of tortuosity. Finally, the representation of a real carbon surface by a perfect graphitic one does not provide the correct prediction of the isosteric heat of adsorption in the low adsorption coverage limit.16 Consequently, because of both practical and fundamental interest in relation to adsorption dynamics and process design, 3D construction of the microstructure of porous carbons is essential. (10) Terzyk, A. P.; Furmaniak, S.; Gauden, P. A.; Harris, P. J. F.; Wloch, J.; Kowalczyk, P. J. Phys.: Condens. Matter 2007, 19, 406208. (11) Petersen, T. C.; Snook, I. K.; Yarovsky, I.; McCulloch, D. G.; O’Malley, B. J. Phys. Chem. C 2007, 111, 802. (12) Nguyen, T. X.; Bhatia, S. K. J. Phys. Chem. B 2004, 108, 14032. (13) Nguyen, T. X.; Bhatia, S. K.; Nicholson, D. Langmuir 2005, 21, 3187. (14) Nguyen, T. X.; Bhatia, S. K. Langmuir 2008, 24, 146. (15) Nguyen, T. X.; Bhatia, S. K. J. Phys. Chem. C 2007, 111, 2212. (16) He, Y.; Seaton, N. A. Langmuir 2005, 21, 8297. (17) McGreevy, R. L.; Putsai, L. Mol. Simul. 1988, 1, 359. (18) Opletal, G.; Petersen, T. C.; McCulloch, D. G.; Snook, I. K.; Yarovsky, I. Mol. Simul. 2002, 28, 927.
10.1021/la800351d CCC: $40.75 2008 American Chemical Society Published on Web 07/01/2008
Atomistic Modeling of ActiVated Carbons
First, Gubbins and workers19–23 constructed atomistic structural models for porous carbons such as activated mesocarbon microbead (a-MCMB) carbons and conducted a series of sacharose char simulations using reverse Monte Carlo (RMC)17 and hybrid reverse Monte Carlo (HRMC).18 Subsequently, Nguyen et al.24 employed a combination of the environmentaldependent interaction (EDIP) potential adapted for carbon by Marks,25 which covers a longer carbon-carbon interaction range up to the interlayer spacing distance of graphite (potential cutoff ) 0.32 nm), and shorter-range reactive empirical bond order (REBO) potential26 (potential cutoff ) 0.2 nm) for the HRMC construction of the microstructure of saccharose char CS1000a. More recently, the HRMC technique has been used by Peterson et al.11 to construct an atomistic structural model of hightemperature heated glassy carbon. Although the RMC- or HRMCconstructed algorithms equipped with short-range carbon potentials (EDIP or REBO) have already been used for the atomistic construction of porous carbons, moderate success can be seen only for rather high density porous carbon (>1.5 g/cm3). This may be due to the fact that such short-range carbon potentials used in the HRMC algorithm are unable to capture the longerrange interatomic interaction induced by the pore structure of low-density carbon such as activated carbon fiber ACF15 (Fc ≈ 0.9 g/cm3). However, the experimental dimensional pair distribution function does not guarantee a unique representation of the 3D microstructure of the carbon. Consequently, the current HRMC method with the use of an arbitrary initial configuration is very time-consuming and even unfeasible for the construction of low-density anisotropic carbons such as ACFs. To improve the current HRMC method, we propose a novel HRMC-constructed algorithm whereby the initial configuration is generated on the basis of the characteristic results (PSD and pore wall thickness distribution) of porous carbons obtained by the interpretation of Ar adsorption at 87 K using the FWT model.1 In this way, the generated initial configuration is expected to be close to the target one and has long-range order, which speeds up the HRMC construction process significantly. The proposed method is applied here to construct an atomistic model of an ACF15 activated carbon fiber provided by the Kynol Corporation investigated in our previous work.2 Finally, we validate our HRMC construction method against experimental adsorption data including the differential heat of adsorption of the simple gases (Ar, N2, CH4, CO2) in the actual ACF15 carbon over wide ranges of temperature and pressure.
2. Experimental Section An ACC-5092-15 (ACF15) activated carbon fiber, provided by the Kynol Corporation, was degassed at 300 °C overnight. The degassed carbon sample was analyzed in an ASAP2010 Micromeritics volumetric adsorption analyzer to obtain the N2 adsorption isotherm at 77 K and the CO2 adsorption isotherm at 273 K, at atmospheric pressure. Subsequently, the degassed sample was also analyzed on a gravimetric sorption system (Rubotherm Pra¨zisionsmesstechnik GmbH, Bochum, Germany) to obtain high-pressure adsorption (19) Thomson, K. T.; Gubbins, K. E. Langmuir 2000, 16, 5761. (20) Pikunic, J.; Clinardv, C.; Cohaut, N.; Gubbins, K. E.; Guet, J. M.; Pellenq, R. J. M.; Rannou, I.; Rouzaud, J. N. Langmuir 2003, 19, 8565. (21) Pikunic, J.; Gubbins, K. E.; Pellenq, R. J. M.; Cohaut, N.; Rannou, I.; Guet, J. M.; Clinard, C.; Rouzaud, J. N Appl. Surf. Sci. 2002, 196, 98. (22) Pikunic, J.; Llewellyn, P.; Pellenq, R. J. M.; Gubbins, K. E. Langmuir 2005, 21, 4431. (23) Jain, S. K.; Pellenq, R. J.M.; Pikunic, J. P.; Gubbins, K. E. Langmuir 2006, 22, 9942. (24) Nguyen, T. X.; Bhatia, S. K.; Jain, S. K.; Gubbins, K. E. Mol. Simul. 2006, 32, 567. (25) Marks, N. A. J. Phys.: Condens. Matter 2002, 14, 2901. (26) Brenner, D. W. Phys. ReV. B 1990, 42, 9458.
Langmuir, Vol. 24, No. 15, 2008 7913 isotherms of CH4 at 310 and 353 K and CO2 at 310 and 333 K for a wide range of pressure up to 200 bar. Detailed information on the gravimetric sorption system was also presented elsewhere.27 For the determination of the structure factor of ACF15 over a wide q range (q ) 4π sin(θ/2)/λ, 0.2 < q
